Chapter 7.5, Problem 76MR

To determine

Todescribe:The pattern for given sequence and to write next three numbers in the sequence.

Answer to Problem 76MR

The pattern of the sequence $\langle s_n\rangle =3,-1,-5,\dots$ is $\langle s_n\rangle =3,-1,-5,-9,-13,-17,\dots ,\left(7-4n\right),\dots$ and next three terms of the sequence are $-9,-13,-17$ .

Explanation of Solution

Given information:

The given sequence is $3,-1,-5,\dots$

Concept used:

A sequence is an arrangement of a list of numbers in a definite order. The numbers forming the sequence are known as its terms. The definite order or the pattern of the sequence

can be expressed by a formula involving natural number n .

Calculations:

The given sequence is $\langle s_n\rangle =3,-1,-5,\dots$ .

The terms of the sequence are in arithmetic progression (AP) whose first term is 3 and common difference is - 4.

The nth term of the AP is $s_n=s_1+\left(n-1\right)\times -4$

  $\Rightarrow s_n=3-4n+4$

  $\Rightarrow s_n=7-4n$

Thus, the sequence may be written as:

  $\langle s_n\rangle =3,-1,-5,-9,-13,-17,\dots ,\left(7-4n\right),\dots$

Hence, next three terms of the sequence $\langle s_n\rangle =3,-1,-5,\dots$ are $-9,-13,-17$ .

Conclusion:

The pattern of the sequence $\langle s_n\rangle =3,-1,-5,\dots$ is $\langle s_n\rangle =3,-1,-5,-9,-13,-17,\dots ,\left(7-4n\right),\dots$ and next three terms of the sequence are $-9,-13,-17$ .